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Nonmodal stability theory. (English) Zbl 1296.76055
Davis, Stephen H. (ed.) et al., Annual review of fluid mechanics. Vol. 39. Palo Alto, CA: Annual Reviews (ISBN 0-8243-0739-9/hbk). Annual Review of Fluid Mechanics 39, 129-162 (2007).
Summary: Hydrodynamic stability theory has recently seen a great deal of development. After being dominated by modal (eigenvalue) analysis for many decades, a different perspective has emerged that allows the quantitative description of short-term disturbance behavior. A general formulation based on the linear initial-value problem, thus circumventing the normal-mode approach, yields an efficient framework for stability calculations that is easily extendable to incorporate time-dependent flows, spatially varying configurations, stochastic influences, nonlinear effects, and flows in complex geometries.
For the entire collection see [Zbl 1106.76006].

76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics